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We propose a method to improve the transmission efficiency and minimize the reflection using graded index metamaterial.By introducing graded index layer at the input and output interfaces between substrate slab and air,the reflection is reduced effectively,meanwhile with the transmission enhanced dramatically.The index profile can be described by a fifth-order polynomial,which ensures the gradient of index at both air and subtract interfaces is equal to zero.I-shaped unit cell has been chosen as the basic cell to realize the graded index impedances matching layer.We investigated the performance of the design by the finite-difference time-domain method with and without the coupler.